The value of $g$ at the surface of earth is $9.8 \,m / s ^2$. Then the value of ' $g$ ' at a place $480 \,km$ above the surface of the earth will be nearly .......... $m / s ^2$ (radius of the earth is $6400 \,km$ )

Suppose the gravitational force varies inversely as the $n^{th}$ power of the distance. Then, the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to

A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, is velocity must be increased ........ $\%$

A tunnel is dug along a diameter of the earth. If $M_e$ and $R_e$ are the mass and radius of the earth respectively. Then the force on a particle of mass $'m'$ placed in the tunnel at a distance $r$ from the centre is

The height at which the weight of a body becomes $1/16^{th}$, its weight on the surface of earth (radius $R$), is

The masses and radii of the earth and the moon are $M_1, R_1$ and $M_2, R_2$ respectively. Their centres are distance $d$ apart. The minimum speed with which particle of mass $m$ should be projected from a point midway between the two centres so as to escape to infinity is